class Solution:
    def minDistance(self, word1: str, word2: str) -> int:
        n, m = len(word1), len(word2)
        dp = [[0] * (m+1) for i in range(n+1)]
        # 初始化边界情况
        for i in range(n+1):
            dp[i][0] = i
        for j in range(m+1):
            dp[0][j] = j
        # 递推所有解
        for i in range(1, n+1):
            for j in range(1, m+1):
                if word1[i-1] == word2[j-1]:
                    dp[i][j] = dp[i-1][j-1]
                else:
                    dp[i][j] = min(
                        dp[i][j-1] + 1,
                        dp[i-1][j] + 1,
                        dp[i-1][j-1] + 1
                    )
        return dp[n][m]